What value of x satisfies the equation 23(6x - 9) + 12(4x + 10) = 3x + 15?

SAT Linear equations in one variable Practice Question 20 (Hard)

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Math · AlgebraHard

What value of $x$ satisfies the equation $\frac{2}{3}(6x - 9) + \frac{1}{2}(4x + 10) = 3x + 15$ ?

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Answer: 16/3

Distribute: $4x - 6 + 2x + 5 = 3x + 15$ . Combine like terms: $6x - 1 = 3x + 15$ . Subtract $3x$ and add 1: $3x = 16$ , so $x = \frac{16}{3}$ .

Writing $\frac{2}{3}(-9)$ as $-3$ instead of $-6$ leads to the incorrect value $\frac{13}{3}$ .

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